Athermal design of nearly incompressible bonds Keith B. Doyle Optical Research Associates, 1800 West Park Drive, Westborough, MA Gregory J. Michels, Victor L. Genberg Sigmadyne, Inc., Rochester, NY ABSTRACT Selecting the proper thickness of high shape factor bonds using near incompressible adhesives is critical to minimize the elastic response of the bonded optical element. For incompressible adhesives with low shape factor, variations in the bond thickness are shown not to be as critical. This is illustrated in the evaluation and redesign of an RTV bond for a primary mirror of a Cassegrain telescope. The initial bond was oversized and highly constrained resulting in focus errors in the telescope during optical testing. Subsequent redesign of the bond thickness to athermalize the design compared various closed-form solutions and finite element parametric studies. Keywords: adhesives, constrained bonds, thin bonds, optical mounting, RTV, finite element analysis, athermal 1. BEHAVIOR OF NEARLY INCOMPRESSIBLE MATERIALS Rubber and rubber-like materials such as RTV are nearly incompressible. Incompressibility is characterized by a Poisson ratio approaching 0.5 and a bulk modulus tending to infinity. Bulk modulus is defined as the relative ability of a material to maintain constant volume under load. It is computed as the ratio of the hydrostatic compressive stress to the decrease in volume. The relationship between the bulk modulus, B, and Poisson ratio, ν, is given by equation 1.1. ( ) ν 2 1 3 − = E B (1.1) For bonds that are characterized by a high shape factor (ratio of the loaded area to the force free area), which is characteristic of thin bonds and/or a mounting geometry that constrains bond deformation, significant forces may be imparted to the optical element due to the effective stiffness of the bond material. Finite-element derived and closed-form equations exist for common bond shapes that relate the compressive stiffness in the direction of the load to the space available for the RTV to deform 1 . The compressive stiffness is often referred to as the compressive modulus. However, the compressive stiffness is not a material property as implied by the modulus term, but a term in the Hooke’s stiffness matrix relating stress and strain. For nearly incompressible bonds with a high shape factor, the value of the compressive stiffness approaches the bulk modulus. In these instances, proper selection of bond thickness is critical in minimizing forces applied to the optical element. 2. RTV DESIGN EXAMPLE An afocal telescope, which acts as a beam expander in a sensing system, experienced focus shifts that exceeded the allowable due to uniform changes in the ambient temperature. A schematic of Optomechanical Design and Engineering 2002, Alson E. Hatheway, Editor, Proceedings of SPIE Vol. 4771 (2002) © 2002 SPIE · 0277-786X/02/$15.00 296
Athermal design of nearly incompressible bonds
Jun 04, 2023
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